ab-angle->ABCF B

Average Error: 31.9 → 22.1

Time: 24.7s

Precision: binary64

Cost: 52672

Math

\[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

↓

\[\begin{array}{l} t_0 := \sqrt[3]{angle \cdot \pi}\\ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(t_0 \cdot \frac{{t_0}^{2}}{180}\right) \end{array} \]

FPCore

(FPCore (a b angle)
 :precision binary64
 (*
  (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0))))
  (cos (* PI (/ angle 180.0)))))

↓

(FPCore (a b angle)
 :precision binary64
 (let* ((t_0 (cbrt (* angle PI))))
   (*
    (* (* -2.0 (+ b a)) (* (- a b) (sin (/ angle (/ 180.0 PI)))))
    (cos (* t_0 (/ (pow t_0 2.0) 180.0))))))

C

double code(double a, double b, double angle) {
	return ((2.0 * (pow(b, 2.0) - pow(a, 2.0))) * sin((((double) M_PI) * (angle / 180.0)))) * cos((((double) M_PI) * (angle / 180.0)));
}

↓

double code(double a, double b, double angle) {
	double t_0 = cbrt((angle * ((double) M_PI)));
	return ((-2.0 * (b + a)) * ((a - b) * sin((angle / (180.0 / ((double) M_PI)))))) * cos((t_0 * (pow(t_0, 2.0) / 180.0)));
}

Java

public static double code(double a, double b, double angle) {
	return ((2.0 * (Math.pow(b, 2.0) - Math.pow(a, 2.0))) * Math.sin((Math.PI * (angle / 180.0)))) * Math.cos((Math.PI * (angle / 180.0)));
}

↓

public static double code(double a, double b, double angle) {
	double t_0 = Math.cbrt((angle * Math.PI));
	return ((-2.0 * (b + a)) * ((a - b) * Math.sin((angle / (180.0 / Math.PI))))) * Math.cos((t_0 * (Math.pow(t_0, 2.0) / 180.0)));
}

Julia

function code(a, b, angle)
	return Float64(Float64(Float64(2.0 * Float64((b ^ 2.0) - (a ^ 2.0))) * sin(Float64(pi * Float64(angle / 180.0)))) * cos(Float64(pi * Float64(angle / 180.0))))
end

↓

function code(a, b, angle)
	t_0 = cbrt(Float64(angle * pi))
	return Float64(Float64(Float64(-2.0 * Float64(b + a)) * Float64(Float64(a - b) * sin(Float64(angle / Float64(180.0 / pi))))) * cos(Float64(t_0 * Float64((t_0 ^ 2.0) / 180.0))))
end

Wolfram

code[a_, b_, angle_] := N[(N[(N[(2.0 * N[(N[Power[b, 2.0], $MachinePrecision] - N[Power[a, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sin[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(Pi * N[(angle / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

↓

code[a_, b_, angle_] := Block[{t$95$0 = N[Power[N[(angle * Pi), $MachinePrecision], 1/3], $MachinePrecision]}, N[(N[(N[(-2.0 * N[(b + a), $MachinePrecision]), $MachinePrecision] * N[(N[(a - b), $MachinePrecision] * N[Sin[N[(angle / N[(180.0 / Pi), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Cos[N[(t$95$0 * N[(N[Power[t$95$0, 2.0], $MachinePrecision] / 180.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 31.9

   \[\left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

2. Simplified 31.9

   \[\leadsto \color{blue}{\left(\left(\left(a \cdot a - b \cdot b\right) \cdot -2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right)} \]
   Proof

   [Start] 31.9	\[ \left(\left(2 \cdot \left({b}^{2} - {a}^{2}\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 31.9	\[ \left(\color{blue}{\left(\left({b}^{2} - {a}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub-neg [=>] 31.9	\[ \left(\left(\color{blue}{\left({b}^{2} + \left(-{a}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 31.9	\[ \left(\left(\color{blue}{\left(\left(-{a}^{2}\right) + {b}^{2}\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   neg-sub0 [=>] 31.9	\[ \left(\left(\left(\color{blue}{\left(0 - {a}^{2}\right)} + {b}^{2}\right) \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-+l- [=>] 31.9	\[ \left(\left(\color{blue}{\left(0 - \left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   sub0-neg [=>] 31.9	\[ \left(\left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right)\right)} \cdot 2\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-lft-neg-out [=>] 31.9	\[ \left(\color{blue}{\left(-\left({a}^{2} - {b}^{2}\right) \cdot 2\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   distribute-rgt-neg-in [=>] 31.9	\[ \left(\color{blue}{\left(\left({a}^{2} - {b}^{2}\right) \cdot \left(-2\right)\right)} \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.9	\[ \left(\left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.9	\[ \left(\left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \left(-2\right)\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   metadata-eval [=>] 31.9	\[ \left(\left(\left(a \cdot a - b \cdot b\right) \cdot \color{blue}{-2}\right) \cdot \sin \left(\pi \cdot \frac{angle}{180}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

3. Taylor expanded in angle around inf 31.9

   \[\leadsto \color{blue}{\left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

4. Simplified 21.9

   \[\leadsto \color{blue}{\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   Proof

   [Start] 31.9	\[ \left(-2 \cdot \left(\left({a}^{2} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.9	\[ \left(-2 \cdot \left(\left(\color{blue}{a \cdot a} - {b}^{2}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   unpow2 [=>] 31.9	\[ \left(-2 \cdot \left(\left(a \cdot a - \color{blue}{b \cdot b}\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   difference-of-squares [=>] 31.9	\[ \left(-2 \cdot \left(\color{blue}{\left(\left(a + b\right) \cdot \left(a - b\right)\right)} \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [=>] 31.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 31.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [<=] 31.9	\[ \left(-2 \cdot \left(\left(\left(a + b\right) \cdot \left(a - b\right)\right) \cdot \sin \color{blue}{\left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [=>] 21.9	\[ \left(-2 \cdot \color{blue}{\left(\left(a + b\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)}\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*l* [<=] 21.9	\[ \color{blue}{\left(\left(-2 \cdot \left(a + b\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right)} \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   +-commutative [=>] 21.9	\[ \left(\left(-2 \cdot \color{blue}{\left(b + a\right)}\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\pi \cdot \left(angle \cdot 0.005555555555555556\right)\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 21.9	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(angle \cdot 0.005555555555555556\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   *-commutative [=>] 21.9	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(0.005555555555555556 \cdot angle\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]
   associate-*r* [<=] 21.9	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

5. Applied egg-rr 21.9

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\frac{angle \cdot \pi}{180}\right)}\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

6. Applied egg-rr 22.1

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\sqrt[3]{angle \cdot \pi}}{\frac{180}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}}\right)} \]

7. Simplified 22.1

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \color{blue}{\left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right)} \]
   Proof

   [Start] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\frac{\sqrt[3]{angle \cdot \pi}}{\frac{180}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}}\right) \]
   unpow2 [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\frac{\sqrt[3]{angle \cdot \pi}}{\frac{180}{\color{blue}{\sqrt[3]{angle \cdot \pi} \cdot \sqrt[3]{angle \cdot \pi}}}}\right) \]
   associate-/r* [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\frac{\sqrt[3]{angle \cdot \pi}}{\color{blue}{\frac{\frac{180}{\sqrt[3]{angle \cdot \pi}}}{\sqrt[3]{angle \cdot \pi}}}}\right) \]
   associate-/l* [<=] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{\sqrt[3]{angle \cdot \pi} \cdot \sqrt[3]{angle \cdot \pi}}{\frac{180}{\sqrt[3]{angle \cdot \pi}}}\right)} \]
   unpow2 [<=] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\frac{\color{blue}{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}}{\frac{180}{\sqrt[3]{angle \cdot \pi}}}\right) \]
   associate-/r/ [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \color{blue}{\left(\frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180} \cdot \sqrt[3]{angle \cdot \pi}\right)} \]
   *-commutative [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \color{blue}{\left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right)} \]

8. Taylor expanded in angle around inf 22.1

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \color{blue}{\sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)}\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]

9. Simplified 22.1

   \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \color{blue}{\sin \left(\frac{angle}{\frac{180}{\pi}}\right)}\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   Proof

   [Start] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(0.005555555555555556 \cdot \left(angle \cdot \pi\right)\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   associate-*r* [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\left(0.005555555555555556 \cdot angle\right) \cdot \pi\right)}\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   *-commutative [<=] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\left(angle \cdot 0.005555555555555556\right)} \cdot \pi\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   /-rgt-identity [<=] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\frac{angle \cdot 0.005555555555555556}{1}} \cdot \pi\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   associate-/l* [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\color{blue}{\frac{angle}{\frac{1}{0.005555555555555556}}} \cdot \pi\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   metadata-eval [=>] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\color{blue}{180}} \cdot \pi\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]
   associate-/r/ [<=] 22.1	\[ \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \color{blue}{\left(\frac{angle}{\frac{180}{\pi}}\right)}\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]

10. Final simplification 22.1

    \[\leadsto \left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle}{\frac{180}{\pi}}\right)\right)\right) \cdot \cos \left(\sqrt[3]{angle \cdot \pi} \cdot \frac{{\left(\sqrt[3]{angle \cdot \pi}\right)}^{2}}{180}\right) \]

Alternatives

Alternative 1
Error	21.9
Cost	26816

\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right)\right) \cdot \cos \left(\pi \cdot \frac{angle}{180}\right) \]

Alternative 2
Error	21.9
Cost	26816

\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right) \]

Alternative 3
Error	22.0
Cost	26816

\[\left(\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\frac{angle \cdot \pi}{180}\right)\right)\right) \cdot \cos \left(\frac{\pi}{\frac{180}{angle}}\right) \]

Alternative 4
Error	22.5
Cost	13833

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -1.06 \cdot 10^{-16} \lor \neg \left(angle \leq 10^{-101}\right):\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(b \cdot b - a \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 5
Error	22.8
Cost	13696

\[\left(-2 \cdot \left(b + a\right)\right) \cdot \left(\left(a - b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.005555555555555556\right)\right) \]

Alternative 6
Error	23.3
Cost	13577

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.31 \lor \neg \left(angle \leq 7500000\right):\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \end{array} \]

Alternative 7
Error	23.3
Cost	13576

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -0.49:\\ \;\;\;\;b \cdot \left(b \cdot \sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right)\right)\\ \mathbf{elif}\;angle \leq 7500000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 8
Error	23.4
Cost	13576

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -1.6 \cdot 10^{-15}:\\ \;\;\;\;\sin \left(angle \cdot \left(\pi \cdot 0.011111111111111112\right)\right) \cdot \left(a \cdot \left(-a\right)\right)\\ \mathbf{elif}\;angle \leq 7500000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot b\right) \cdot \sin \left(\left(angle \cdot \pi\right) \cdot 0.011111111111111112\right)\\ \end{array} \]

Alternative 9
Error	24.6
Cost	7816

\[\begin{array}{l} t_0 := \left(b + a\right) \cdot angle\\ \mathbf{if}\;angle \leq -90:\\ \;\;\;\;\left(angle \cdot \pi\right) \cdot \left(0.011111111111111112 \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;angle \leq 14200000000:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(b \cdot t_0 - a \cdot t_0\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	30.2
Cost	7432

\[\begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+49}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+86}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b - a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 11
Error	30.2
Cost	7432

\[\begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+49}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+86}:\\ \;\;\;\;0.011111111111111112 \cdot \left(\left(angle \cdot \pi\right) \cdot \left(b \cdot b - a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 12
Error	38.2
Cost	7177

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-10} \lor \neg \left(a \leq 4.4 \cdot 10^{-61}\right):\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot 0.011111111111111112\right)\right)\right)\\ \end{array} \]

Alternative 13
Error	33.0
Cost	7177

\[\begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-64} \lor \neg \left(b \leq 5 \cdot 10^{-15}\right):\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \mathbf{else}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \end{array} \]

Alternative 14
Error	32.9
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -9 \cdot 10^{-63}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 2.05 \cdot 10^{-16}:\\ \;\;\;\;angle \cdot \left(-0.011111111111111112 \cdot \left(a \cdot \left(a \cdot \pi\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 15
Error	33.0
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{-64}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\left(angle \cdot -0.011111111111111112\right) \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 16
Error	33.0
Cost	7176

\[\begin{array}{l} \mathbf{if}\;b \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;\pi \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot angle\right)\right)\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-14}:\\ \;\;\;\;-0.011111111111111112 \cdot \left(angle \cdot \left(\pi \cdot \left(a \cdot a\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(angle \cdot 0.011111111111111112\right) \cdot \left(b \cdot \pi\right)\right)\\ \end{array} \]

Alternative 17
Error	43.9
Cost	6912

\[0.011111111111111112 \cdot \left(angle \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right) \]

Alternative 18
Error	43.9
Cost	6912

\[0.011111111111111112 \cdot \left(\pi \cdot \left(angle \cdot \left(b \cdot b\right)\right)\right) \]

Alternative 19
Error	43.9
Cost	6912

\[angle \cdot \left(0.011111111111111112 \cdot \left(b \cdot \left(b \cdot \pi\right)\right)\right) \]

Alternative 20
Error	43.9
Cost	6912

\[angle \cdot \left(\pi \cdot \left(b \cdot \left(b \cdot 0.011111111111111112\right)\right)\right) \]

Reproduce

herbie shell --seed 2023125 
(FPCore (a b angle)
  :name "ab-angle->ABCF B"
  :precision binary64
  (* (* (* 2.0 (- (pow b 2.0) (pow a 2.0))) (sin (* PI (/ angle 180.0)))) (cos (* PI (/ angle 180.0)))))